67
67

Sep 17, 2013
09/13

by
L. Vitagliano

texts

######
eye 67

######
favorite 0

######
comment 0

We extend the geometric Hamilton-Jacobi formalism for hamiltonian mechanics to higher order field theories with regular lagrangian density. We also investigate the dependence of the formalism on the lagrangian density in the class of those yelding the same Euler-Lagrange equations.

Source: http://arxiv.org/abs/1003.5236v1

42
42

Sep 19, 2013
09/13

by
L. Vitagliano

texts

######
eye 42

######
favorite 0

######
comment 0

We formalize geometrically the idea that the (de Donder) Hamiltonian formulation of a higher derivative Lagrangian field theory can be constructed understanding the latter as a first derivative theory subjected to constraints.

Source: http://arxiv.org/abs/1009.6054v2

34
34

Sep 21, 2013
09/13

by
L. Vitagliano

texts

######
eye 34

######
favorite 0

######
comment 0

We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.

Source: http://arxiv.org/abs/0905.4580v2

37
37

Sep 18, 2013
09/13

by
L. Vitagliano

texts

######
eye 37

######
favorite 0

######
comment 0

The covariant phase space of a Lagrangian field theory is the solution space of the associated Euler-Lagrange equations. It is, in principle, a nice environment for covariant quantization of a Lagrangian field theory. Indeed, it is manifestly covariant and possesses a canonical (functional) "presymplectic structure" w (as first noticed by Zuckerman in 1986) whose degeneracy (functional) distribution is naturally interpreted as the Lie algebra of gauge transformations. We propose a...

Source: http://arxiv.org/abs/0809.4164v5

37
37

Sep 23, 2013
09/13

by
L. Vitagliano

texts

######
eye 37

######
favorite 0

######
comment 0

We define partial differential (PD in the following), i.e., field theoretic, analogues of hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD-Hamilton equations, PD-Noether theorem, PD-Poisson bracket, etc.. Unlike in standard multisymplectic approach to hamiltonian field theory, in our formalism the geometric structure (kinematics) and the dynamical information on the "phase space" appear as just different components of one single...

Source: http://arxiv.org/abs/0903.4528v2

39
39

Sep 21, 2013
09/13

by
L. Vitagliano

texts

######
eye 39

######
favorite 0

######
comment 0

Diffieties formalize geometrically the concept of differential equations. We introduce and study Hamilton-Jacobi diffieties. They are finite dimensional subdiffieties of a given diffiety and appear to play a special role in the field theoretic version of the geometric Hamilton-Jacobi theory.

Source: http://arxiv.org/abs/1104.0162v2

32
32

Sep 19, 2013
09/13

by
A. M. Vinogradov; L. Vitagliano

texts

######
eye 32

######
favorite 0

######
comment 0

In the preceding note math.DG/0610917 the $\Lambda_{k-1}\mathcal{C}$--spectral sequence, whose first term is composed of \emph{secondary iterated differential forms}, was constructed for a generic diffiety. In this note the zero and first terms of this spectral sequence are explicitly computed for infinite jet spaces. In particular, this gives an explicit description of secondary covariant tensors on these spaces and some basic operations with them. On the basis of these results a description...

Source: http://arxiv.org/abs/math/0703661v1

32
32

Sep 19, 2013
09/13

by
A. M. Vinogradov; L. Vitagliano

texts

######
eye 32

######
favorite 0

######
comment 0

For the multiple differential algebra of iterated differential forms (see math.DG/0605113 and math.DG/0609287) on a diffiety (O,C) an analogue of C-spectral sequence is constructed. The first term of it is naturally interpreted as the algebra of secondary iterated differential forms on (O,C). This allows to develop secondary tensor analysis on generic diffieties, some simplest elements of which are sketched here. The presented here general theory will be specified to infinite jet spaces and...

Source: http://arxiv.org/abs/math/0610917v1

49
49

Sep 18, 2013
09/13

by
A. M. Vinogradov; L. Vitagliano

texts

######
eye 49

######
favorite 0

######
comment 0

We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed context and, in particular, enriches it with new natural operations. Applications will be considered in subsequent notes.

Source: http://arxiv.org/abs/math/0605113v1

65
65

Sep 19, 2013
09/13

by
A. M. Vinogradov; L. Vitagliano

texts

######
eye 65

######
favorite 1

######
comment 0

Basic elements of integral calculus over algebras of iterated differential forms, are presented. In particular, defining complexes for modules of integral forms are described and the corresponding berezinians and complexes of integral forms are computed. Various applications and the integral calculus over the algebra $\Lambda_{\infty}$ will be discussed in subsequent notes.

Source: http://arxiv.org/abs/math/0610914v1

53
53

Sep 19, 2013
09/13

by
A. M. Vinogradov; L. Vitagliano

texts

######
eye 53

######
favorite 0

######
comment 0

We describe the first term of the $\Lambda_{k-1}\mathcal{C}$--spectral sequence (see math.DG/0610917) of the diffiety (E,C), E being the infinite prolongation of an l-normal system of partial differential equations, and C the Cartan distribution on it.

Source: http://arxiv.org/abs/math/0703761v1

49
49

Jul 20, 2013
07/13

by
A. M. Vinogradov; L. Vitagliano

texts

######
eye 49

######
favorite 0

######
comment 0

A natural extension of Riemannian geometry to a much wider context is presented on the basis of the iterated differential form formalism developed in math.DG/0605113 and an application to general relativity is given.

Source: http://arxiv.org/abs/math/0609287v1

23
23

Sep 22, 2013
09/13

by
R. Ruffini; L. Vitagliano; S. -S. Xue

texts

######
eye 23

######
favorite 0

######
comment 0

The dynamical properties of an electron--positron--photon plasma created by the vacuum polarization process occurring around a charged gravitationally collapsing core of an initially neutral star are examined within the framework of General Relativity and Quantum Field Theory. The Reissner--Nordstr\"{o}m geometry is assumed to apply between the collapsing core and the oppositely charged remnant of the star. The appearance of a separatrix at radius $\bar{R}$, well outside the asymptotic...

Source: http://arxiv.org/abs/astro-ph/0309022v1

25
25

Sep 19, 2013
09/13

by
R. Ruffini; L. Vitagliano; S. -S. Xue

texts

######
eye 25

######
favorite 0

######
comment 0

We describe electron-positron pairs creation around an electrically charged star core collapsing to an electromagnetic black hole (EMBH), as well as pairs annihilation into photons. We use the kinetic Vlasov equation formalism for the pairs and photons and show that a regime of plasma oscillations is established around the core. As a byproduct of our analysis we can provide an estimate for the thermalization time scale.

Source: http://arxiv.org/abs/astro-ph/0304306v1

36
36

Sep 19, 2013
09/13

by
R. Ruffini; L. Vitagliano; S. -S. Xue

texts

######
eye 36

######
favorite 0

######
comment 0

We describe the creation and evolution of electron-positron pairs in a strong electric field as well as the pairs annihilation into photons. The formalism is based on generalized Vlasov equations, which are numerically integrated. We recover previous results about the oscillations of the charges, discuss the electric field screening and the relaxation of the system to a thermal equilibrium configuration. The timescale of the thermalization is estimated to be $\sim 10^{3}-10^{4} \hbar...

Source: http://arxiv.org/abs/astro-ph/0302549v2

24
24

Sep 19, 2013
09/13

by
R. Ruffini; L. Vitagliano; S. -S. Xue

texts

######
eye 24

######
favorite 0

######
comment 0

We describe the evolution of an electron-positron-photon plasma created by Sauter--Heisenberg--Euler--Schwinger mechanism around a collapsing charged star core in the Reissner-Nordstr\"{o}m geometry external to the core, in view of the application in the framework of the EMBH theory for gamma ray bursts.

Source: http://arxiv.org/abs/astro-ph/0304307v1

31
31

Sep 20, 2013
09/13

by
R. Ruffini; F. Fraschetti; L. Vitagliano; S. -S. Xue

texts

######
eye 31

######
favorite 0

######
comment 0

We present theoretical predictions for the spectral, temporal and intensity signatures of the electromagnetic radiation emitted during the process of the gravitational collapse of a stellar core to a black hole, during which electromagnetic field strengths rise over the critical value for $e^+e^-$ pair creation. The last phases of this gravitational collapse are studied, leading to the formation of a black hole with a subcritical electromagnetic field, likely with zero charge, and an outgoing...

Source: http://arxiv.org/abs/astro-ph/0410233v1

33
33

Sep 19, 2013
09/13

by
R. Ruffini; C. L. Bianco; P. Chardonnet; F. Fraschetti; L. Vitagliano; S. -S. Xue

texts

######
eye 33

######
favorite 0

######
comment 0

If due attention is given in formulating the basic equations for the Gamma-Ray Burst (GRB) phenomenon and in performing the corresponding quantitative analysis, GRBs open a main avenue of inquiring on totally new physical and astrophysical regimes. This program is one of the greatest computational efforts in physics and astrophysics and cannot be actuated using shortcuts. A systematic approach has been highlighted in three paradigms: the relative space-time transformation (RSTT) paradigm, the...

Source: http://arxiv.org/abs/astro-ph/0302557v1